Signal processing and the control of physical systems generally involves obtaining measurements from a physical system in the form of electrical signals and processing the signals in order to bring about a desired result. For example, the control of a physical system typically involves obtaining measurements from the physical system, comparing the measurements with a predetermined control recipe, and adjusting the system inputs in response to the comparison to minimize variations between the measured values and recipe values. During signal processing and control, the signals to be processed or the variables to be controlled, which ever the case may be, are not always directly available for observation and must be inferred from indirect and noisy measurements. The indirect measurements are generally obtained from embedded sensors which contain multiple pieces of information that are dynamically confounded. Extraction of the information of interest requires the use of complex and time consuming calibration procedures and the use of estimating techniques that result in high computation costs. Equipment setup costs are also high since diagnostic measurements must be taken to correlate the measured signal to the indirect measurements for each piece of equipment.
In addition, measurements from a physical system are not always obtainable at a single time interval (time scale). For example, there may be a first measurement that is obtainable only at a first time scale, a second measurement that is only obtainable at a second time scale, a third measurement that is only obtainable at a third time scale, and so on. In other instances, a measurement, or a set of measurements, taken from a physical system may not bear the same spatial relationship with the system as other measurements taken from the system. Even in instances where all measurements are available at a single high rate, the computation cost of indirect measurements at the high rate can be very high.
Often, the task of controlling a system involves not only the control of a single physical system, but the control of a family of physical systems. This situation is most prevalent in high volume manufacturing applications. The characteristics of a single physical system tend to change over time due to equipment degradation and other causes. Moreover, the characteristics between a family of physical systems tend to differ from one physical system to another due to equipment-to-equipment variations. It is important to track these changes and to account for these differences so that the signal processing or control system may be updated accordingly. Otherwise, the accuracy of the signal processing or control system is compromised.
Current signal processing and control systems do not provide for the rapid calibration of such systems, nor do they have the ability to track changes in the characteristics of a single physical system or a family of physical systems.
Thus, what is needed is an accurate and cost efficient method of processing signals generated within a physical system, or a family of physical systems, in which measurements are obtained at different time scales and/or different space scales.